SOURCE-WEIGHTED DOMAIN INTEGRAL APPROXIMATION FOR LINEAR TRANSIENT HEAT-CONDUCTION

In employing the Boundary Element Method (BEM) to solve linear transie nt heat conduction problems, domain integrals need to be calculated. T hese integrals are generated by initial or pseudo-initial conditions a nd can be calculated directly by discretizing the domain. The need for domain meshing undermines the elegance of the boundary element approa ch and so a number of techniques have been developed in an attempt to overcome this. The most recent of these being the Multiple and Dual Re ciprocity methods. This paper is concerned with a new approach which i nvolves the direct approximation of fundamental solutions using linear combinations of sources positioned at different points in time. The w eighting associated with each source is determined by minimization of the maximum absolute error using a single point exchange algorithm. In this way it is possible to determine the domain integrals to a high d egree of accuracy with minimal computational effort. Error bounds for the approximation are naturally provided by the error reduction proced ure giving an indication of the number of sources required for accurat e domain integrals. The procedure is developed in detail for two and t hree-dimensional parabolic integral equations. Accuracy and stability are examined and the results of numerical tests are presented.